How do you write an exponential equation that passes through (-1, .5) and (2, 10)?

1 Answer
Aug 5, 2015

I found: #color(red)(y=0.5e^(1+x)#

Explanation:

In general the equation will be of the form:
#y=ke^(cx)#
where: #k and c# are constants to be found:
let us use our points and substitute into our general equation:
#{(0.5=ke^(-c)),(10=ke^(2c)):}#
from the first:
#k=0.5/e^-c=0.5e^c#
substitute into the second:
#10=0.5e^c*e^(2c)#
use the law of exponents and get:
#e^(c+2c)=10/0.5=20#
take the #ln# on both sides:
#3c=ln(20)#
#c~~1#
substitute back into #k=0.5/e^-c=0.5e^c#:
#k=0.5e#
so finally your equation will be:
#color(red)(y=0.5e*e^x=0.5e^(1+x)#

Graphically:
enter image source here